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Journal of Control Science and Engineering 4 (2016) 61-70 doi: 10.17265/2328-2231/2016.02.002

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Analytical Modeling and Experimental Validation of Electromagnetic Field Radiated by In-house PLC Lines D. Chariag1 , J-C. Le Bunetel1 , K. Khalil1 , Y. Raingeaud1 , M. Machmoum2 and P. Guerin2 1. GREMAN: Research Group on Materials, Microelectronics, and Acoustic Nanotechnology, University of Tours, Tours 37200, France 2. IREENA: Institute of Research on Electrical Energy of Nantes-Atlantic, University of Nantes, Nantes 44300, France Abstract: Broadband PLC (power line communication) technology is a main factor of the development of digital convergence in the indoor network. It uses the already existing power cable infrastructure for communication purposes. The EM (electromagnetic) field radiating from the cable could, however, disturb other communication systems, and thus should be evaluated. The M oM (method of moment) and the FEM (finite element method) have been studied to estimate the EM field emitted from the power cable. However, the M oM is difficult to treat the dielectric material of the cable and the FEM is time consuming. This paper presents a new approach to estimate the radiated EM fields caused by PLC systems from the CM current along the cable, based on the transmission line theory. The proposed model has the advantage of using the measured primary parameters of the cable. An experimental analysis of the EM radiation distribution is also presented. A comparison showed that the model results agree quit e well with the measurements performed in this study. Key words: PLC, EM field, transmission line theory, primary parameters.

1. Introduction PLC (power line communication) technologies use the power line cable as the transmission line for both high data rate applications and control systems. The development of this technology is enhanced by the publication of the IEEE standard (IEEE Std 1901™-2010) [1]. This standard provides a minimum implementation subset that allows a fair coexistence of the BPL (broadband over power line) devices. It also complies with EMC (electromagnetic compatibility) limits set by the national regulators. EMC of PLC systems deals with two aspects. The first aspect is related to the susceptibility of the system in the presence of noise, and especially of impulsive noise [2]. This type of noise has been extensively characterized in the literature [3-10]. Zimmermann and Dostert classified the noise in PLC channels into Corresponding author: Jean-Charles Le Bunetel, professor, research fields: transmission lines, communication power line, smart grid, EM C.

five classes [3, 4]. A statistical model of the impulsive noise is proposed in Refs. [5, 6]. An estimation of the background noise is performed and presented in Ref. [7]. The periodic asynchronous impulsive noise is pointed out in Ref. [8]. In Ref. [9], the noise in narrowband PLC is expressed as a Gaussian process. In summary, there is a good understanding of the noise characteristics over indoor PLC channels. Nowadays, thanks to the optimization of modulation techniques and coding schemes, new PLC devices are generally able to deal with the different type of noises. The second aspect of EMC of PLC systems is related to the emissions generated by these systems. For conducted emissions, the PLC signal is seen as a useful signal and there are few works dealing with the susceptibility of the household appliances to the PLC signal. However, numerous recent studies, which were carried out to analyze the coexistence between PLC systems and VDSL2 (very high bit-rate digital subscriber line) ones, showed that the radiated emissions from the PLC signal can lead to a decrease

62

Analytical Modeling and Experimental Validation of Electromagnetic Field Radiated by In-house PLC Lines

of the QoS (quality of service) of VDSL2 transmissions [11-15]. For example, it is indicated in

dipole model [30]. The presented model is validated with measurements using commercial PLC modems.

Ref. [11] that the mutual impact of PLC and VDSL2 systems depends on the distance between electrical

The remainder of this paper is organized as follows: in Section II, a detailed description of the

and phone lines, the length of the cables, the coexistence length, and the network imbalance.

measurement set-up is given. The HF (high frequency) model of the considered network is described in

In order to mitigate the radiated emissions from

Section III. The mathematical model of the radiated

PLC systems, several studies have been made. The authors in Ref. [16-19] investigated the emission

EM field is presented in Section IV. Section V provides a comparison between the simulated EM

levels of existing PLC systems and compared them to the EMC standards such as FCC, EN55022 and NB30.

fields and the experimental ones. Finally, Section VI concludes this paper.

Indeed, the radiation mainly depends on the CM (common mode) current [20]. This current is due to electrical asymmetries and to the LCL (longitudinal

2. Measure ment Set up The radiated EM field was measured using the

conversion loss) [20, 21]. An analysis of the DM (differential mode) to CM current conversion process

experimental set-up as shown in Fig. 1. The measurement was carried out in an anechoic chamber

in power line networks can be found in Ref. [22]. There has been a lot of theoretical modeling for

of length and width equal to 9.2 m and 7.6 m, respectively. The measured frequency range was from

radiated emissions from PLC systems [23-29]. Several

0.15 MHz to 30 MHz. The electric and magnetic

methods have been used to compute the EM field such as the four-port network method [29], the MoM [28]

fields were measured separately using monopole and loop antennas. This allows near-field measurements.

and the so-called wire grid model [27]. Calculating the radiated field using the four-port

The height of the antenna is 1.7 m and the horizontal distance from the electrical cable is 1.0 m. The

network method cannot only be based on the CM

antenna output voltage was measured using a spectral

current [28]. The method of moment cannot consider the influence of the dielectric material of the cable.

analyzer. The analyzer was installed outside the anechoic chamber and was connected to the antenna

The so-called wire grid model (based on the electro-static theory [28]) computes the

using a coaxial cable. Our purpose is to replicate the real operating

per-unit-length RLCG (resistance, inductance, capacitance, conductance). The RLC parameters are calculated from analytical expressions. The last

conditions of a PLC connection in the semi-anechoic chamber. To this end, the PLC signal was injected using two HPAV (Home Plug AV) modems (offers a

parameter “G” is deduced from measurements. The calculation results using these methods do not

physical layer peak data rate of 200 Mbits/s). In the indoor PLC network, the transmitter (PLC modem) is

sufficiently agree with the measured ones. This paper proposes an appropriate calculation model for the radiated EM field from PLC lines. Firstly, the RLCG parameters of electrical cable considering the ground

connected on one side to an ADSL (asymmetric digital subscriber line) modem using the Ethernet cable and on the other side to the electrical grid. To replace the ADSL connection, the ADSL modem is

wire are extracted from measurements. Then, these

connected to a video server using a DSLAM

parameters are used by the SPICE simulator to calculate the CM current distribution along the cable. Finally, the EM field is deducted using infinitesimal

(digital subscriber line access multiplexer). A category 5 cable is used between the DSLAM and the ADSL modem.

Analytical Modeling and Experimental Validation of Electromagnetic Field Radiated by In-house PLC Lines Power cable

Ethernet cable

Câble électrique

Réseau Electrical électrique network

Phone cable

Câble Ethernet

63

Video cable

Câble téléphonique plat

Câble vidéo

DSLAM

6m m 6.5

1.5 m

1,2m

Phone Réseau téléphonique network Modem ADSL (IAD)

X 1,7m

Y

Fig. 1

Réseau Electrical électrique Filter network Filtre

40cm

Serveurserver vidéo Video

RSIL LISN

Modem CPL PLC

STB

Ecran de TV TV LCD

The experimental set-up.

The presented network is connected to the power grid through an LISN (line impedance stabilizer network), a low pass filter

and

an

isolation

transformer. This reduces the EM noise from the power network.

3. High Frequency Model of the Power Network

Fig. 1 depicts the experimental network. The

The distribution of the CM current should be calculated to estimate the radiated EM field. In this paper, the CM current distribution was simulated using the LTspice software. The simulation was

electrical cable is attached to a wooden support

carried out using the RLCG parameters of the power

forming a rectangular loop at a height of 0.4 m from the ground level (Fig. 2).

cable, the LC (inductance and capacitance) model of the multi-plug and the measured impedances of the connected devices (TV, video box, modems). This section details the model of these components (power

Fig. 2

A photo of the experimental grid.

The horizontal and vertical lengths of the loop are respectively 1.5 m and 6.5 m, so the total length is 16.0 m. The power cable is made up of three wires (phase, neutral and ground) coated in insulating PVC. Adding a ground wire is important to take into

cable, multi-plug, connected devises). 3.1 Power Cable Model

account the propagation noise in the CM signal. The cross-section area of the wire is 2.5 mm 2 . The ADSL

The power cables can be described and modeled using the transmission line theory. In this theory, the

modem and the transmitter PLC modem are plugged

power cable is considered as a series of elementary

into

the same

cells, each representing a short segment of the

multi-plug. The receiver PLC modem, the TV and the

transmission line. As shown in Fig. 3, every cell can be described by the so-called primary line parameters, usually denoted as RLCG. The type of the power

the electrical network

through

video box are connected to the grid using a second multi-plug as shown in Fig. 1.


64

is fully described in Ref. [31]. Next, an electrical circuit is assigned for each parameter (R(f)-L-C-G(f)) as shown in Fig. 4. In order to improve the model accuracy, the value of each electrical component is realized using genetic algorithms [32]. 3.2 HF Model of the Multi-plug Fig. 3 Model of a three-conductor cable with the primary parameters.

The multi-plug comprises two parts: the exterior part which is the cable and the interior one which

cable concerned by the present study is RVV 3G 2.5 mm². The length of the elementary cell is equal to

includes two bus-bar, as shown in Fig. 5. The primary RLCG parameter of a 25.0 cm cell is deduced from

25.0 cm in the 1 to 50 MHz frequency range. It should

open and short measurements method described in Ref.

be noted that the length of the elementary segment must be chosen as a function of the studied frequency

[31]. The bus-bar is divided into segments of 10 cm as

range. Indeed, this length should be negligible compared to the shortest wavelength; for a maximum

shown in Fig. 5. The open and short measurements method was applied to calculate the primary

operating

parameters of the bus-bar segment. The R and G parameters are not considered in modeling the bus-bar.

frequency of 50

MHz,

the shortest

wavelength is about 4.0 m. There are several methods to estimate the value of

Indeed, the copper and the dielectric losses of the

the primary parameters, based on analytical expressions, finite element simulation or experimental

considered bus-bar are very small. The measurements show that the values of L and C parameters are

measurements [31]. In this paper, the RLCG parameters are extracted from measurements in the 1 to 50 MHz frequency range. The measurement process

constant for all measured frequencies (L = 17.7 nH and C = 2.65 pF). Fig. 6 shows the circuit model of the multi-plug (includes 5 plugs). R4=2.57

R(f) - L R3=0.157 R2=47m L1=65nH R1=0.023

C //G(f)

L3=3.58nH

L2=3.38nH L1=6.19nH

C1=0.165p

C2=0.25pF

F

C=8pF

R1=100M 

Fig. 4

Equivalent circuit of primary parameters RLCG.

R2=1.3M 

R3=40k

Analytical Modeling and Experimental Validation of Electromagnetic Field Radiated by In-house PLC Lines Distance between two plugs 10cm

65

Segmen t

2.5cm

Bus-bar

Ground-bar

Fig. 5

Photo of the multi-plug bus-bar.

Plug

Fig. 6

Plug

Plug

Plug

Plug

Model of the bus-bar.

Magnitude of the open circuit impedance

Z (Ω)

Model Measure

Frequency (Hz) Fig. 7 Comparison between measured and modeled impedances of the bus-bar.

Fig. 7 shows a comparison between measured and modeled impedances of the bus-bar. A good

network (TV, ADSL modem, video box and the LISN) are modeled using their measured impedances. In fact,

agreement between the two plots can be seen. For the sake of simplicity, the ground bus is not considered in

an arbitrary voltage source in the LTspice software is controlled using a mathematical expression or a data

the model. The experimental

two

file. In this work, a measurement database file is used to control the arbitrary voltage source.

multi-plugs. Both the ADSL modem and transmitter

The measurement set-up of the household appliances

network

comprises

PLC modem are connected to the first multi-plug. The TV and the video box are connected to the second one. These devices are modeled using the measured impedances. 3.3 HF Model of the Connected Appliances The appliances connected to the experimental

is described in Ref. [33] and depicted in Fig. 8. 3.4 Experimental Validation of the Modeled Network The network model (shown in Fig. 1) is built using the LTspice software as shown in Fig. 9. The power cable is modeled using the primary RLCG parameters. The multi-plug is modeled using the primary parameters

66


simulation file. To validate the frequency model of the network, the transmission parameter S21 between two points is measured and compared to the simulation. The results are presented in Fig. 10. A similar trend is observed between the simulated and the measured transmission Fig. 8

Impedance measurement test bench.

parameter. However, a deviation of 5 dB is noted

described previously. The measured impedances of the connected devices are integrated in the

around the frequency of 22 MHz. A low deviation is also detected around 35 MHz.

Cable model Multi-plug model

Fig. 9

Fig. 10

LTspice model of the experimental network.

Comparison between measured and simulated S 21 parameter.


4. Analysis of the Radiated EM Fields As described in the literature, the PLC radiation is mainly depending on the CM current [20]. So, the elementary cell of the three-conductor cable acts as a thin wire (very small radius compared to the length) and the assumption of infinites imal dipole can be used. In fact, the length of the elementary cell (25 cm) is much smaller than the shortest wavelength up to 30 MHz. Assuming that the current is located at the z-axis ( I  I 0 u z ), and the distance of the observation point (M(r, θ, φ)) from the origin is r, as shown in Fig. 11. The vector potential is given by Eqs. (1) and permeability of vacuum and the dipole. Aφ is zero when

in spherical coordinates (2), where μ0 is the 𝑙 = 𝑑𝑧 is the length of the current is located at

67

The magnetic field in Eq. (4) and the electric field in Eq. (6) are valid everywhere except on the source itself (cable). The EM fields vary according to the distance r between the dipole and the observation point. Depending on this distance, three regions are identified: the near field region (k. r < 1), the middle region (k. r ≥ 1) and the far field region (k. r >> 1). T o evaluate the EM fields radiated from the network (depicted in Fig. 1), the circuit model (Fig. 9) was simulated using the LTspice software. The PLC modem is modeled using a 50 Ω impedance in parallel w ith an AC voltage s ourc e (port 1). For eac h elementary cell, the simulated CM current was used to calculate the EM fields according to Fig. 12. Eqs. (4) z

the z-axis. The magnetic field is calculated through Eqs. (1-3). Ar  0 I 0l cos( )

e  jkr 4r

(1)

A    0 I 0l sin( )

e  jkr 4r

(2)

1  A  H  A  ( rA )  r u  0 0 r  r   1

M

r  dz

y ö

(3)

Substituting Eqs. (1) and (2) in Eq. (3) reduces the

φ x

magnetic field to: H  j

kI0l sin( )  1   jkr , H   H r  0 (4) 1  jkr  e 4r  

Fig. 11 Hx 

Infinitesimal dipole.

 Hx

i

Hy 

i 1

The electric field is obtained from the vector potential Eqs. (1) and (2) using Eq. (5). E   j A  j

1

 0 0

(  A ) 

1

 0 0

 H

 Hy

Hz 

i

i 1

 Hz

i

i 1

H  Hx2  Hy2  Hz 2

(5)

Hxn

Hx1 Hxi Hy1

In spherical coordinates, we have:  I 0l cos(  )  1   jkr 1 e  Er    2 2r jkr     kI0l sin(  )  1 1   jkr 1  e  E  j  4r jkr ( kr )2    E  0,   

where η is the impedance of free space (η = 120π).

Observation point

Hz1

Hyi

Hyn Hzn

Hzi I1 Ii

(6)

Elementary cell

Fig. 12

In

Analysis model of radiating magnetic field.


68

and (6) are transferred to Cartesian coordinates. The total field is the vector sum of the fields radiated from each elementary cell.

well with that of the calculated ones for all frequencies.

6. Conclusion

5. Comparison between the Model and the Measure ment

In this paper, we addressed the issue of radiated emissions caused by in-house PLC systems based on

Fig. 13 shows the comparison between the

experimental measurements. The measurements were

measured magnetic field and the calculated one using the proposed model. Two regions are identified from

performed inside an anechoic chamber in a frequency band up to 30 MHz. A new approach to estimate the

this comparison. The first region includes two frequency bands from 150 kHz to 2 MHz and from 10

radiated EM fields from PLC systems using the transmission line theory was provided. The proposed

MHz to 13 MHz. A large gap is noted between the

model allows the calculation of the radiated EM field

model and the measurement for these frequency bands. For the 150 kHz to 2 MHz band, these errors can be

components from the CM current along the cable by considering the ground conductor. The model has the

justified. Indeed, the background noise and the noise generated by the connected devices are not taken into

advantage of using the primary parameters extracted from the measurement. This allows to reduce the

account in the model. The second region includes frequencies from 2 MHz to 10 MHz and from 13 MHz

modeling errors compared to other methods such as analytical and numerical calculations ones. The

to 30 MHz. A good agreement can be noted between

comparison between experiment and model results

measurement and model results for this region. Fig. 14 shows the measured and calculated electric

showed that the model can provide good EM interference predictions in PLC.

field distributions. The measured values agreed quite

The aim of future studies is to extend the model up to 100 MHz. Other type of cable could also be

Measure H (dBμA/m)

Model

modeled.

Acknowledge ments This research was supported by the French Region Center with the MDE MAC3 project funding.

References Frequency (Hz)

Fig. 13

[1]

Radiated magnetic field. Measure

[2]

E (dBμV/m)

Model

[3]

[4] Frequency (Hz)

Fig. 14

Radiated electric field.

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